Determine the limit of the function (sin5x-sin3x)/x, x-->0

We have to
find the value of lim x--> 0[ (sin 5x - sin 3x)/x]

if we substitute x = 0,
we get the form 0/0, which allows us to use the l'Hopital's rule and substitute the numerator
and the denominator by their derivatives.

=> lim x--> 0[ 5*cos 5x -
3*cos 3x]

substitute x = 0

=> 5*1 - 3*1

=> 2

The required value of lim x-> 0[ (sin 5x -
sin 3x)/x] = 2